February 3rd, 2015. 
Prof. Michel Bercovier (Hebrew University of Jerusalem)
"Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes"

 Tuesday, February 3rd, 2015 at 3 pm in the Conference Room of IMATI-CNR, Pavia.


We solve the following problem: given a polynomial of order $n$ and the corresponding Bezier tensor product patches over an unstructured regular quadrilateral mesh with nodes of any valence, find a solution to the $G^{1}1$ or $C^{1}1$ approximation (resp. interpolation ) problem.
Constraints defining regularity conditions across patches have to be satisfied. The resulting number of free degrees of freedom must be such that for instance the interpolation problem has a solution. This is similar to studying the minimal determining set (MDS) for a $C^{1}1$ continuity construction.
We consider a given arbitrary quadrilateral mesh, that can include a cubic boundary curve and the final surface approximation or PDE solution is obtained by energy methods. We completely solve the problem and show that there is always a solution for $n\ge 5$ and under some mesh restrictions for $n=4$.
From a practical point of view, the present work provides a way to build first order smooth interpolation/approximation and solutions to partial differential equations for arbitrary structures of quadrilateral meshes.
We will also discuss how this work can contribute to IGA, in the light of a recent result by J. Peters. (Joint work with Tanya Matskewich)


The Applied Mathematics Seminar usually meets on Tuesdays at 3 pm in the Conference Room of IMATI-CNR, Pavia. Refreshments are offered after the talk. For further information, please contact the organizers Carlo Lovadina, Stefano Lisini and Laura Spinolo.